Colloquium: Robert Bryant -- From Mechanics to Algebra and Geometry: The origins of holonomy

Title: From Mechanics to Algebra and Geometry: The origins of holonomy 
Carslaw 173

Abstract: : Familiar mechanical phenomenon, such as driving and parking a car, rolling a
ball, and even the ability of falling cats to land on their feet (usually) are examples
of an underlying mathematical concept that, in the 19th century, became to be known as
`holonomy’.  As it became better understood, mathematicians and physicists began to
realize that holonomy underlay many different phenomena, from the everyday situations
mentioned above to understanding the curvature of space in Einstein’s theory of general
relativity.  Currently, holonomy lies at the heart of both deep mathematical objects and
high-energy physical theories, such as string theory and the still-mysterious M-theory,
on which many theoretical physicists would like to base a ’theory of everything’.  

In this talk, after discussing some holonomic phenomena in everyday life, I’ll explore
their underlying commonality and their appearance in more advanced situations and try to
provide some insight into why this idea has turned out to be so fundamental.

We will go for lunch after the talk.